Convert Grid Squares to Fractions: Identifying 5/7 from Visual Model

Q: How do I know if I'm counting squares or just lines?

Look for enclosed rectangular regions, not just the lines that separate them. Each square is a complete box with 4 sides. The grid lines are just the boundaries between squares.

Q: What if some squares look different sizes?

All squares in this type of problem are equal parts of the whole, even if they appear slightly different due to screen display. Focus on counting the number of regions, not their visual appearance.

Q: Why isn't the answer 5/6 if there are 6 spaces between lines?

Those are gaps between lines, not the actual squares! Count the enclosed regions (squares) created by the grid. There are 7 squares total, with 5 shaded.

Q: Should I count from left to right or does order matter?

Order doesn't matter for counting! You can count systematically (left to right) to avoid missing any, but the total will be the same. Just make sure you count each square exactly once.

Q: How can I double-check my counting?

Use the equation: shaded + unshaded = total. If 5 + 2 = 7, then your fraction $ \frac{5}{7} $ is correct!

Visual Fraction Models with Grid Division

Write the fraction shown in the drawing:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from visual representation to mathematical representation of the fraction

00:03 Count the division cells of the whole (denominator)

00:11 Count the number of colored parts (numerator)

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction shown in the drawing:

Step-by-step solution

To solve the problem, we will follow these steps:

Step 1: Count the total number of equal parts shown in the drawing.
Step 2: Count the number of shaded parts in the drawing.
Step 3: Form the fraction using the number of shaded parts over the total number of parts.

Now, let's address these steps in detail:

Step 1: Count the total equal parts.
From the drawing, it appears there are 7 equal parts.

Step 2: Count the shaded parts.
There are 5 shaded parts highlighted in the drawing.

Step 3: Write the fraction.
Now, we write the fraction as:
$\frac{5}{7}$

This fraction represents the shaded area of the total, therefore the solution to the problem is $\frac{5}{7}$ .

Final Answer

$\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Counting Rule: Count total grid squares first, then shaded squares
Technique: Write fraction as shaded parts over total parts: 5 shaded out of 7 total
Check: Verify by counting again: 5 shaded squares + 2 unshaded = 7 total squares ✓

Common Mistakes

Avoid these frequent errors

Counting only visible grid lines instead of complete squares
Don't count the 6 vertical lines as the denominator = $\frac{5}{6}$ instead of correct answer! Lines create squares, but the fraction represents parts of the whole. Always count the actual square regions formed by the grid lines.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

$\frac{10}{7}=$

FAQ

Everything you need to know about this question

How do I know if I'm counting squares or just lines?

Look for enclosed rectangular regions, not just the lines that separate them. Each square is a complete box with 4 sides. The grid lines are just the boundaries between squares.

What if some squares look different sizes?

All squares in this type of problem are equal parts of the whole, even if they appear slightly different due to screen display. Focus on counting the number of regions, not their visual appearance.

Why isn't the answer 5/6 if there are 6 spaces between lines?

Those are gaps between lines, not the actual squares! Count the enclosed regions (squares) created by the grid. There are 7 squares total, with 5 shaded.

Should I count from left to right or does order matter?

Order doesn't matter for counting! You can count systematically (left to right) to avoid missing any, but the total will be the same. Just make sure you count each square exactly once.

How can I double-check my counting?

Use the equation: shaded + unshaded = total. If 5 + 2 = 7, then your fraction $\frac{5}{7}$ is correct!

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